Problem 52 - Algebra 1: Concepts and Skills

Question

OPERATIONS WITH DECIMALS Find the value of the expression. $$ 32.8-4 $$

Step-by-Step Solution

Answer

The value of the expression \(32.8 - 4\) is \(28.8\)

Step 1: Analyze the Given Expression

The given expression is \(32.8 - 4\). Here, we are subtracting a whole number (4) from a decimal number (32.8). This is a simple arithmetic operation involving subtraction of two numbers.

Step 2: Perform the Subtraction

Subtract the whole number 4 from the decimal number 32.8. It is important to preserve the decimal position correctly in the result. The decimal number 32.8 equals 32.8 hence it is just as though you were subtracting the number 4 from the number 32. This results in \(28.8\). The decimal place in 32.8 is maintained in the solution.

Key Concepts

Operations with Decimals

Decimals are numbers that have parts beyond the whole number, usually shown after a dot or 'decimal point'. Performing operations with decimals, such as addition, subtraction, multiplication, and division, involves understanding how to align these decimal points properly. A crucial point is that when performing these operations, you align numbers so that their decimal points match up.

This is especially highlighted in subtraction, where aligning the decimals ensures that place values, like units, tenths, hundredths, etc., line up correctly. This alignment is critical to getting the right answer. Decimals are used frequently in everyday life, such as in money or measurements, so being proficient with these operations can be very helpful.

Arithmetic Operations

Arithmetic operations form the foundation of mathematics, consisting of addition, subtraction, multiplication, and division. Each of these has specific rules and procedures, but they all serve the purpose of combining numbers and understanding their relationships. When we think about arithmetic operations with decimals, it involves specific attention to the decimal points.

Subtraction, like other operations, changes slightly when decimals are involved. In the problem tagged as 32.8 - 4, it's crucial to ensure that the decimal part of 32.8 is preserved throughout the calculation. As arithmetic operations come to terms with numbers and their decimal values, maintaining clarity between whole numbers and decimal parts can lead to successful and accurate computation.

Subtraction of Whole Numbers from Decimals

When subtracting a whole number from a decimal, such as in our example of 32.8 minus 4, you are essentially taking away 4 whole units from 32 full units and then leaving the decimal in place. When performing this operation, it's key to focus on maintaining the decimal point accurately within the aligned numbers.

Here's how it goes:

• Start by writing down the decimal number, 32.8.
• Line up the whole number, 4, with the last whole digit of the decimal, as if it were 4.0.
• Perform the subtraction just like you would with whole numbers, ensuring to drop the decimal point straight down into your answer.

The result of this process is 28.8. By subtracting 4 from the integer portion (32) and keeping the decimal part unchanged, the solution accurately reflects the arithmetic operation performed.